key: cord-0805731-vkgtzyom authors: Kuo, Fei-Ying; Wen, Tzai-Hung title: Regionalization for infection control: An algorithm for delineating containment zones considering the regularity of human mobility date: 2020-12-09 journal: Appl Geogr DOI: 10.1016/j.apgeog.2020.102375 sha: bfa72662dc5fe291f7b1de9ed8882c600a845491 doc_id: 805731 cord_uid: vkgtzyom Restricting human movement to decrease contact probability and frequency helps mitigate large-scale epidemics. Movement-based zoning can be implemented to delineate the boundaries for movement restrictions. Previous studies used network community detection methods, which capture cohesive within-region movements, to delineate containment zones. However, most people usually travel and spend most of their time in several fixed locations, which implies that an infected person could transmit the pathogens to only a specific group of people with whom s/he usually has a contact in frequently-visited locations. Existing network community detection methods cannot reflect the regularity of the flow of people; thus, this study aims to use land-use patterns to reflect trip purposes to measure the regularity of human mobility. We propose a novel network community detection method, the Human Mobility Regularity-based Zoning (HuMoRZ) algorithm, to delineate containment zones incorporating mobility regularity. The Taipei metropolitan area in Taiwan is used to demonstrate the feasibility of the proposed algorithm. The spatial diffusion of an emerging respiratory disease, novel influenza A/H1N1, is simulated for comparing three different quarantine zoning systems: (1) a minimum zoning unit, (2) optimal zoning without considering mobility regularity, and (3) optimal zoning considering mobility regularity. Two epidemiological performance indicators are used to compare simulation results: namely, the accumulated infected number (AN) on the 30th day, reflecting the severity of an epidemic, and the critical time (CT), the moment at which half of the population becomes infected, measuring the diffusion speed of an epidemic. To measure the variety of different facility types within a containment zone, we further use Shannon's entropy scores, representing a self-contained zone, and the boxplot of all zones' entropy scores, reflecting geospatial homogeneity of life functions across zones. Our results suggest that containment zones that incorporate mobility regularity could significantly delay the epidemic peak and critical time and decrease the severity of an epidemic. The zoning patterns proposed in our algorithm could also allow for more life functions in a zone and more evenly distributed life resources across zones than those of zones generated by other methods. These findings could provide insightful implications for fighting the COVID-19 pandemic. Epidemic diffusion is usually aggravated by human or animal movements because their movements increase the contact probability and the frequency between infected entities and healthy entities (Fèvre, Bronsvoort, Hamilton, & Cleaveland, 2006; Mao, 2014) . Thus, restricting their movements to decrease such probability and frequency helps control and mitigate epidemics (Bajardi et al., 2011; Velthuis & Mourits, 2007) . In practice, movement restriction is a common measure used to earn time to develop effective vaccines or drugs when an emerging infectious disease appears (Gensini, Yacoub, & Conti, 2004) . The effectiveness of movement restrictions against global epidemics, including influenza A/H1N1 (Cooper, Pitman, Edmunds, & Gay, 2006; Epstein et al., 2007) , SARS (T. Day, Park, Madras, Gumel, & Wu, 2006; Fraser, Riley, Anderson, & Ferguson, 2004) , and Ebola virus (Peak et al., 2018) , has also been proven in previous studies. Movement restrictions are usually separated into two different modes: isolation and quarantine (Barbera et al., 2001; Day et al., 2006; Fraser et al., 2004) . Both of these two modes control the movements of infected entities, but quarantine also restricts high-risk asymptomatic entities, who may have contacted infected entities, to their living neighborhoods. However, when the number of confirmed cases grows exponentially, it is difficult to comprehensively trace all contacts for quarantine and further epidemiological investigations (Fong et al., 2020; Peak et al., 2020) . In this situation, quarantine tends to focus on delineating a certain geographical area to cover all possible contacts. This mass quarantine approach, also named containment, is the strictest approach to preventing epidemic diffusion (Wilder-Smith, Chiew, & Lee, 2020) . Large-scale containment was implemented to control the diffusion of the COVID-19 epidemic in 2020. The Chinese government progressively implemented city lockdowns in Wuhan and nearby cities (Wu, Leung, & Leung, 2020) . However, citywide containment could raise two concerns. First, widespread containment may frighten residents and cover many individuals with no significant risk of diseases (Barbera et al., 2001; Rubin & Wessely, 2020) ; thus, it could cause social panic and increase the infection probability of low-risk individuals within the city. High social panic may prompt people to resist quarantine policies or to flee (Coltart, Lindsey, Ghinai, Johnson, & Heymann, 2017) , which generates loopholes in epidemic prevention. Second, containment requires enormous resources, including medical and security services, to sustain the lives of people in containment areas (Barbera et al., 2001) . Although China has successfully implemented citywide containment in Wuhan, this approach may not be feasible in many other countries because few countries can completely imitate China's strategies due to different political systems . On the other hand, megacities in China, such as Beijing and Shanghai, implemented another, less strict containment policy during the COVID-19 pandemic: "closed-off management" (Shao, 2020) . A microdistrict (e.g., residential unit) is regarded as a control unit for restricting people's movement when a confirmed case appears in this microdistrict. However, it is difficult to effectively contain an epidemic to a small-scale containment zone, such as microdistrict closed-off management, because exposed contacts may occur in different microdistricts (Barbera et al., 2001) . Furthermore, some infectious diseases, such as COVID-19 or MERS, can be transmitted asymptomatically (Omrani et al., 2013; Rothe et al., 2020) . Thus, before being quarantined, an infected person may transmit infectious pathogens to many other individuals. These exposed individuals, who are not in containment zones, may become the next spreaders. In summary, neither the citywide level nor the microdistrict level may be the appropriate spatial scale for containment. An appropriate containment zone should include the places where an infected person usually stays and the places where exposed individuals frequently visit; it should also efficiently sustain the lives of people in quarantine. Recent literature developed a movement-based zoning approach to delineating containment zones to confront foot-and-mouth disease (FMD) (G.-J. Lee, Pak, Lee, & Hong, 2019) . A network structure was implemented to formulate livestock movement, where the nodes were livestock facilities, and the links were the amount of livestock transportation among different facilities. Then, a network community detection method was used to group livestock facilities into several communities. A community is a group of certain nodes that strongly interact with each other but weakly interact with the nodes in other communities (Malliaros & Vazirgiannis, 2013) . If an outbreak of FMD occurs in a livestock facility, a network community could capture the infected facility and other high-risk livestock facilities. Thus, a network community can be used for delineating containment zones for FMD outbreaks. Similar to livestock transportation, human movements from any one place to another could also be formulated as a network. This network reflects the aggregated movement behavior of a group of people, and a zone delineated by existing network community detection methods captures intensive human movements (Liu, Gong, Gong, & Liu, 2015; Zhong, Arisona, Huang, Batty, & Schmitt, 2014) . A delineated community could include all possible contacts once an infected person identified, and this community may be a zone mixing high-risk and low-risk contacts. Thus, the size may be too large to be an appropriate containment zone for restricting human movement. Theoretically, in an urban area, a person may regularly encounter identical people, including his or her friends and some familiar strangers (Sun, Axhausen, Lee, & Huang, 2013) . The reason is that most people usually travel short distances and return to a few frequently visited locations, such as their homes or workplaces, with a high probability (González, Hidalgo, & Barabási, 2008; Song, Koren, Wang, & Barabási, 2010) . In other words, most people usually travel and spend most of their time in several fixed locations (Song, Qu, Blumm, & Barabási, 2010) , thereby representing a spatially constrained movement pattern (Belik, Geisel, & Brockmann, 2011) . Therefore, the regularity of flows of people implies that an infected person, before being quarantined, could transmit pathogens to only a specific group of people with whom s/he usually has contact in frequently visited locations. Since existing network community detection methods cannot reflect the regularity of the flow of people, this study aims to incorporate the regularity of urban human mobility within a city into network community detection to delineate better containment zones for disease control. We propose a novel network community detection method, the Human Mobility Regularity-based Zoning (HuMoRZ) algorithm, for considering urban-scale daily routines. It is based on the map equation algorithm, a commonly used community detection method for directed and weighted graphs (Rosvall & Bergstrom, 2008) . We use the population flow of the Taipei metropolitan area, one of the major East Asian cities, as a case study to demonstrate the effectiveness and feasibility of the proposed algorithm. An epidemic diffusion model is used to simulate the spatial dynamics of disease transmission with different movement restriction scenarios to compare the performance of zoning algorithms. As delineating containment zones for movement restrictions are usually considered to be implemented to block the spread of high-infectivity diseases, our simulation focuses on the intervention scenarios of high-infectivity disease transmission. We propose a mobility regularity-based zoning algorithm for detecting network communities. The concept is based on the random walker's long-term movement behaviors among the nodes of a human movement network to evaluate any given pattern of communities. In addition to strong interactions within a community and weak interactions between communities, our objective also pursues high levels of regular within-community movements. We adopt the optimization approach of the map equation algorithm to optimize the number of communities to which each node belongs. The procedure involves finding new network community patterns by following searching strategies and checking whether new patterns can improve the objective value. The final result is the one whose objective value is the smallest and cannot be further improved by new patterns. For detailed descriptions of the optimization procedure, refer to Rosvall, Axelsson, and Bergstrom (2009) . The proposed zoning algorithm incorporates mobility regularity into the objective function to find the optimal patterns of network communities. Regularity describes individuals' daily routine movement behaviors such as commuting or grocery shopping (Schneider, Belik, Couronné, Smoreda, & González, 2013) . However, a population flow network cannot reflect individual-level trajectories, movement behaviors, and trip purposes. Recent studies have shown that land-use functions can be used to reveal trip purposes (M. Lee & Holme, 2015; Maat, Van Wee, & Stead, 2005) ; thus, we adopt the movement patterns within land-use functions as a proxy to measure mobility regularity. The details of measuring mobility regularity are as follows. In Fig. 1 , we illustrate the concept of estimating the probability of each specific purpose when the random walker moves from one place to another. The number 0.2 is the conditional probability that the random walker moves from α to β given that it is currently in α. This probability is then separated into three parts based on the proportion in the area of three different land-use types in β. Each part represents a conditional probability of a specific trip purpose. Eq. (1) and Eq. (2) denote the general form of this estimation. where α is an origin and β is a destination. p α is the probability that the random walker visits node α. ω αβ is the conditional probability that the random walker goes to β, given that it is currently in α. z k β is the area proportion of the kth land-use type in β. Here, p α ω αβ is the total probability moving from α to β, and we separate this probability into K parts based on the area proportion of K land-use types so that each part can represent the probability of a specific trip purpose. In this study, we focus on within-community movements to measure mobility regularity that results from daily routines. In other words, people repeatedly go to one place for the same purpose. For example, most people have only one fixed location for work, and people usually go to a few familiar restaurants to have a meal. Therefore, mobility regularity implies that travel for a specific purpose originating from one place should not be evenly distributed among other destinations but rather concentrate on just some of them. Our measurement is based on this implication. Fig. 2 compares two different zoning scenarios. In scenario (A), when the random walker leaves node α, the probability of each travel purpose concentrates on one place. In contrast, each probability is evenly distributed on two destinations in scenario (B). To measure this concentration, we adopted Shannon's entropy score. A low value reflects a high level of concentration (Eq. (3) and Eq. (4)); furthermore, Eq. (5) denotes the measurement of mobility regularity. , α, β ∈ the same community (3) An example demonstrating how we use different land-use types to reflect trip purposes in a human movement network. Suppose that the random walker moves to β with probability 0.2 when it leaves α; we separate this probability into three parts based on the area proportions of three different land-use types in β. Therefore, 0.04, 0.1, and 0.06, respectively, represent the probabilities of residential, commercial, and industrial purposes for the movement of the random walker from α to β. where p k α represents the intracommunity probability that the random walker leaves α but stays within the same community because of the kth trip purpose. Note that we utilize only the flow originating from to its groupmates, the nodes belonging to the same community as α, to measure the entropy. Additionally, β can equal α if self-loops exist. Each node contains at most K entropy values; thus, we use a weighted entropy score representing the compound effect of these K values. For each trip purpose, we weight its entropy value (H(Z k a )) by its intracommunity probability (p k α ) and then summarize these weighted entropy values (Eq. (5)). When the IR(α) value is larger; the movement behaviors of the random walker originating from α for each trip purpose show more destinations within a community. In contrast, a smaller value of IR(α) reflects that the movement behavior toward one specific destination is more concentrated, which represents mobility regularity. Therefore, IR(α) can be regarded as the inverse regularity level. Finally, combining the original objective function of the map equation (L(M)) with the summation of the inverse regularity level of all nodes yields the objective function of our new algorithm (Eq. (6)). We minimize the value of the objective function to find the optimal pattern of network communities. To compare the zoning performance of HuMoRZ algorithm, we compare our results with the random zoning method, which randomly assigns locations into different zones with the same zones number of HuMoRZ's result. The random zoning is repeatedly simulated 99 runs to capture the possible combinations of random assignment. To check whether our HuMoRZ algorithm can delineate an effective zoning system for infectious disease containment, we compare three different zoning methods: (1) a minimum zoning unit (a traffic analysis zone (TAZ), noted as "TAZ-scale"), (2) optimal zoning without considering mobility regularity (the result of the map equation, noted as "without regularity"), and (3) optimal zoning considering mobility regularity (the result of our proposed HuMoRZ algorithm, noted as "with regularity"). Two dimensions are evaluated for the comparison. The first is the effect of different zoning methods on slowing down epidemic progression; the other is the level of self-containment (diversity of life functions) that different zoning methods allow zones to possess. To evaluate the effect on blocking contagion spread in an epidemic, we simulate the spatial diffusion of an emerging respiratory disease, novel influenza A/H1N1. The simulation is implemented under different epidemic scenarios by a four-state susceptible-latent-infective-removed (SLIR) model, modified from Wen, Hsu, Sun, Jiang, and Juang (2018) , as shown in Eq. (7) to Eq. (11). An example demonstrating how we use entropy to measure mobility regularity for each node. In scenario (A), α, β, and γ compose a zone. When the random walker leaves α and goes to β or γ (i.e., it still stays in this zone) for a specific trip purpose, entropy helps to determine whether the random walker tends to go to one place or go to β and γ on average. The random walker tends to go to β for commercial purposes and go to γ for industrial purposes. This pattern displays typical movement behaviors. On the other hand, in scenario (B), α, δ, and ε compose another zone. For every trip purpose, no clear tendency indicates the preferred destinations when the random walker leaves α, so a regular pattern of movements does not exist. Our inverse-regularity index (IR(α)) in scenario (A) is lower than the index value in scenario (B), so this index can help indicate whether a within-zone movement pattern is regular. are the number of susceptible, latent, infective, and removed individuals at time t and place i. N i is the population number of place i, and W(j, i) is the amount of human movement from place j to place i. β is the average transmission rate defining the transmissibility of a disease; θ is the latent rate determining how fast a latent case can infect others; γ is the removed (recovery) rate representing the speed of transformation from infective to removed. We adopt the same three parameters values used in Wen et al. (2018) : β = 0.585/ day, θ = 0.32/day, and γ = 0.09/day. We assume that the subpopulation number (N i ) in each place i does not change over time, which reflects urban daily routine movement such as commuting or going shopping. Most people moving to other places will return to their residential places within one day; thus, the subpopulation number may not significantly vary between different days. Recent studies also adopted this similar assumption (Gatto et al., 2020; Tang et al., 2020) . Under this assumption, our Eqs. (7) and (11) capture the dynamics of possible pathogen transmissions when infected people move to other places in the daytime. To examine all possible scenarios with different initial outbreak locations, we change the initial outbreak location by turns and repeat the epidemic simulation (a total of 498 runs, reflecting the number of locations in our study). In each simulation, the initial condition is composed of the initial outbreak location and five latent locations. The latent locations represent the locations with the undetected infected persons and these locations strongly interact with the origin of the outbreak. In our simulation, the quarantine intervention is implemented on only one specific containment zone where the initial outbreak occurs. Three different quarantine levels (80%, 90% and 99%) are tested to reflect different strictness of movement restrictions. The 99% level means that only 1% of the original travel amount is allowed to enter and leave the containment zone and is regarded as the strictest level in this study. Two epidemiological performance indicators are used to assess each simulated result. The first one is the accumulated infected number (AN) on the 30th day, reflecting the severity of an epidemic. Recent studies also adopted this similar indicator (Malavika et al., 2020) . The other indicator is the critical time (CT), at which half of the population becomes infected. It reflects the diffusion speed of an epidemic. Finally, we collect all categories of point-of-interest (POI) locations, such as government agencies, cultural and educational facilities, medical and funeral facilities, public and memorial places, life function facilities such as convenience stores and supermarkets, and transportation facilities. Every category is further divided into several different types, and a total of 83 subtypes are incorporated into our study. Shannon's entropy score is used to capture various types of POIs within a containment zone (Eq. (12)). where n k i is the number of the kth POI type in zone i, and N i is the total POI number in zone i. A containment zone with a high entropy value indicates that the POIs within this zone could provide various life functions, thereby representing a high level of the self-contained zone. Thus, an appropriate zoning pattern should ensure most zones with high entropy values so that residents could maintain their everyday lives as much as possible, even being quarantined. The Taipei metropolitan area in Taiwan is used to demonstrate the feasibility of the proposed HuMoRZ algorithm. The Taipei metropolitan area is the political and economic center of Taiwan. This area covers approximately 2457.13 square kilometers of land and has a population of approximately 7.03 million, which is 30% of the total population of Taiwan. Public transportation systems include one international airport, three HSR (high-speed rail) stations, thirteen train stations, 125 mass rapid transit (MRT) stations, approximately 600 bus lines, and over 1000 public bicycle sharing (PBS) stations (Ministry of Transportation and Communications in Taiwan, 2020). The land use data are from the National Land Surveying and Mapping Center (NLSC) of Taiwan for 2012. The spatial extent of this dataset covers the major part of the Taipei metropolitan area, specifically, approximately 1362.57 square kilometers of land and a population of approximately 6.34 million. This dataset is a three-level hierarchical classification system whose primary classification contains nine categories: agriculture, forest, transportation, water conservation, building, public facility, recreation, strip mining, etc. We adopt the finest-scale classifications because they reflect the most detailed human activity categories and trip purposes. A total of 79 land-use types are incorporated in this study. The human mobility data are from the fourth version of the "Taipei Rapid Transit Systems Demand Model" (TRTS-Ⅳ), an official survey conducted by the Department of Rapid Transit Systems (DORTS) of the Taipei City Government in 2009. This dataset divides the entire Taipei metropolitan area into 508 traffic analysis zones (TAZs). The average area of a TAZ is 2.74 km 2 , with an average population of 12,732 people. There are a total of 498 TAZs covered in our study, including downtown and suburban areas (Fig. 3) . The transport authority investigates the daily number of people traveling from any one TAZ to another. It also provides the estimated amounts of travel in 2012 (Fig. 4) ; thus, these data correspond with the land use dataset on both spatial and temporal dimensions. Based on the human traveling data and land use data, our HuMoRZ algorithm separates 498 TAZs into 26 containment zones, averagely covering 19 TAZs with an average population density of approximately 8500 people per square kilometer (Fig. 4) . Fig. 5 further displays the histogram of TAZ numbers and population density among 26 containment zones. It shows that only two zones are composed of over thirty TAZs, and eight zones possess a high population density of over 10,000 people per square kilometer. Moreover, the comparison between our zoning result and the random zoning method in Fig. 6 demonstrates that HuMoRZ can also reveal pivotal characteristics of network communities: strong within-community and weak between-community interactions. Fig. 7A shows the spatial distribution of different boundary types of containment zones delineated by HuMoRZ. It shows that the main roads (avenues) partition different zones in downtown areas, while the suburban areas are partitioned by natural landforms, including mountain ridges and rivers. Moreover, Fig. 7B shows that the significant boundary types are Ridge, River, or Road. Fig. 8 further demonstrates the spatial distribution and the length proportion of different boundary types of TAZs. By comparing the proportions of boundary types between Figs. 7 and 8, the difference of boundary types indicates that the zoning result of HuMoRZ could highlight more barrier effects, including natural boundaries (River, and Ridge) and artificial boundaries (Road), to restrict human movement than TAZs. Fig. 9 compares the zoning patterns generated by our HuMoRZ algorithm and the existing method, the map equation algorithm. The difference in zoning patterns arises from whether mobility regularity is considered in an algorithm. The map equation only considers flow intensity and cycling performance. Thus, the result shows that all downtown areas become one huge zone covering a large number of TAZs; the other TAZs located in peripheral urban areas constitute several small zones, which reflect isolated lifestyles in remote areas. The zoning pattern resulting from the map equation in Fig. 9B is its finest scale; in other words, the map equation cannot further divide the huge zone into different smaller zones. In contrast, our algorithm produces similar zoning patterns in the peripheral areas but partitions central downtown areas into several compact zones, each of which is connected by higher within-zone flows (Fig. 4) . We compare the progression dynamics of a respiratory disease based on three containment zoning modes and distinct quarantine levels in Fig. 10 . The zoning pattern from the map equation, which does not consider mobility regularity, is analogous to a citywide lockdown because it groups the whole downtown area into one huge zone. In contrast, every TAZ as a containment zone is similar to microdistrict closed-off management. The scale of the zones generated by our HuMoRZ algorithm falls between that of these two zoning systems. The results show that our zoning mode can more effectively slow down the spread of an epidemic than the other two zoning modes. The effect of delaying the epidemic peak is more significant as the quarantine level becomes stricter. Under the strictest quarantine level (Fig. 10C) , our zoning mode can delay the peak by approximately one week. Fig. 11 shows the comparison between three zoning modes based on epidemic severity (accumulated infected number on the 30th day, denoted as AN) and spreading speed (the time it takes to for half of the population to be infected, noted as CT). Through comparing the scenarios with different initial outbreak locations and quarantine levels, Fig. 11 indicates that the zoning result of HuMoRZ shows the lowest AN and the highest CT among the three zoning modes. Fig. 12 displays distributions of POI entropy values of three different zoning modes, respectively. It shows that the regularity-based containment allows most zones to possess higher life functions (higher entropy value) than the microdistrict containment (TAZ-scale). Moreover, compared to the citywide containment (zoning without regularity) or the microdistrict containment, the regularity-based containment possesses the lowest spatial inequality of the life function diversity because of the shorter interquartile range (IQR) of the entropy values than other methods. In other words, neither microdistrict containment nor citywide containment can provide appropriate life functions within every zone and raises the issues of spatial inequality of life resources. In this study, we used land-use patterns to reflect trip purposes for measuring human mobility's regularity and proposed the HuMoRZ algorithm, which incorporates mobility regularity into network community detection, to delineate containment zones for infection control. Our results demonstrate more compact zones delineated by the HuMoRZ algorithm than those generated by existing algorithms and identify different types of barriers to restricting human movement. In other words, artificial infrastructures and natural landforms essentially shape the geographic extent of human mobility. Moreover, the results also show that our zoning system can significantly reduce epidemic severity in the early stage and has a positive effect on delaying the epidemic peak. Our movement restriction scenario helps figure out that quarantining only the initial outbreak location is not enough to contain an epidemic effectively. Our results also demonstrate that large-scale containment, such as quarantining all the city, is also not the optimal measure to contain an epidemic. It is challenging to implement effective individual quarantine for continuously increasing case incidence in the whole city. Therefore, our results show that containment zones incorporating mobility regularity have the optimal effect on delaying peak time and decreasing the severity of an epidemic. Furthermore, the extent of our containment zones can also reflect the high diversity of POI types, allowing for various life functions and geographic homogeneity of life resources among zones. In sum, HuMoRZ's zoning pattern shows better outcomes than other existing containment approaches in terms of allowing a diversity of life functions and delaying epidemic peaks. The sizes of the containment zones delineated by the HuMoRZ algorithm may also be more appropriate than those generated by existing methods. Barbera et al. (2001) argued that both large-scale and small-scale containment are not effective approaches. Large-scale containment, such as city lockdown represented by our without-mobility-regularity simulation scenario, makes it difficult to support the whole population in a city with medical and human resources. While this approach was successful in confronting the COVID-19 epidemic in Hubei Province, China, scholars argued that this approach might not be feasible in other countries because of different political institutions . On the other hand, small-scale containment, such as microdistrict closed-off management, may miss some asymptomatically infected people and allow disease transmissions to keep occurring outside containment zones; such a phenomenon has occurred in the COVID-19 epidemic in the U.S. (Parodi & Liu, 2020) . The factor generating our compact zoning pattern is the inclusion of mobility regularity, which implies that people usually display spatially constrained movement patterns despite their potentially high mobility (Belik et al., 2011) . Thus, these constrained movement behaviors spatially connect several local places and form compact zones (Farmer & Fotheringham, 2011) . In the COVID-19 epidemic, Italy was the first outbreak country in Europe, yet the government launched containment approaches too late (Indolfi & Spaccarotella, 2020) . The early inaction may have been the result of economic considerations. The decision to implement a city lockdown poses a tradeoff between public health and the nation's economy (Auzan, 2020) . Our HuMoRZ algorithm may provide a solution to this tradeoff problem. The epidemic simulation results (Figs. 10 and 11) demonstrate that the zoning pattern of HuMoRZ algorithm could significantly reduce the case number at the beginning of an epidemic and delay the time of the epidemic peak. This delay earns health authorities more time to prepare and deploy medical resources for implementing control measures against an epidemic (Desjardins, Hohl, Fig. 4 . The zoning result of HuMoRZ algorithm. The flows whose amount is less than one hundred are removed in this figure for better visualization. These flows are still used in analysis and zoning. & Delmelle, 2020). Therefore, by blocking an appropriate zone at the initial epidemic stage, the Italian government could have gained more time to prepare prevention resources such as mask-wearing or environmental disinfection. Then, the epidemic could have been contained within the confinement zone, and the national economy may not have been dramatically affected. showing when half of the population is infected; moreover, dots indicate every epidemic peak, which is when the prevalence rate reaches the highest level. Some infectious diseases, such as MERS or COVID-19, can transmit pathogens to susceptible hosts before symptom occurrence (Omrani et al., 2013; Rothe et al., 2020) . In other words, a diagnosed case can infect others before the onset of illness or even any apparent symptoms; such invisible spreaders have caused social panic in Italy (M. Day, 2020) . To identify these invisible spreaders, high numbers of testing per capita have been adopted during the COVID-19 pandemic in many countries, such as South Korea and Germany . Nonetheless, this approach involves cost-effectiveness issues, and not all countries or local governments can implement comprehensive screening and testing . Therefore, we argue that zoning based on regular contact patterns and delineation of the local spatial extent of contact among individuals could help narrow down possible close contacts and high-risk exposure to prioritize the deployment of screening and testing resources. Our zoning pattern, which shows a self-contained life circle and is geographically homogeneous, echoes the concept of functional regions in the human geography literature. A functional region is described as a life circle consisting of many places with different land-use types where the residents can acquire almost all daily necessities (Philbrick, 1957) . Based on this self-contained characteristic of their region, people seldom need to travel across boundaries to other regions, and a cohesive movement pattern exists within each functional region (Klapka & Halás, 2016) . Such human movement patterns and land use diversity allow a functional region to act as an independent containment zone because people can survive well without interacting with others in another region. Moreover, while the level of self-containment increases as a functional region becomes larger, a large functional region will lose strong inner cohesion of movements (Halás, Klapka, & Erlebach, 2019) . Therefore, a functional region cannot be either too large or too small, in line with the aforementioned suggestion of Barbera et al. (2001) regarding the size of a containment zone. As our HuMoRZ algorithm can divide a region into compact self-containment zones, it could also be appropriate for delineating functional regions. A functional region could resemble a containment zone; however, existing methods focus only on cohesive within-region movements and weak between-region movements (Halás et al., 2019) and neglect diverse land-use types sustain daily lives. The land-use patterns could reflect different trip purposes of daily routines and are further used to measure mobility regularity. Thus, the HuMoRZ algorithm takes a step further to incorporate land use patterns into the partitioning of cohesive groups of a human mobility network. Our study has some limitations. First, our zoning pattern is confined to TAZs, which are spatial units used in this study; these TAZs do not have equal size, shape, and land area. Although previous studies also delineate zones within an urban area based on small-scale administrative districts (Goddard, 1970) , uniform grids could be a better resolution for calculating the movement amount between any two grids. However, it needs to aggregate detailed individual-level travel routes from GPS tracking data, which is difficult to access. Second, this study adopts agglomerated travel amounts to represent residents' level of interactions between two different locations. It cannot reflect individual-level travel frequency and regularity. Moreover, our travel amount only considers the two-dimensional surface area of land use and ignores the vertical dimensions, such as floor area in buildings and skyscrapers (Frank, Bradley, Kavage, Chapman, & Lawton, 2008) . It could underestimate the travel amount related to in-door activities such as traveling to a department store for shopping or traveling to an office building for work. Therefore, floor area data should be included to measure mobility regularity better. Third, strangers may be in close proximity to each other for a long time on a bus or in a subway carriage, but such contacts do not exist if individuals use their private vehicles (Cooley et al., 2011) . In other words, people have different contact patterns and epidemic risks based on their transport types (Andrews, Morrow, & Wood, 2013) . It warrants further investigation considering various transport types. Last but not least, although most people move regularly, different demographic groups may have different movement behaviors. For example, the movements of women are usually shorter than those of men (Verhetsel, Beckers, & De Meyere, 2018) , and low-income people seldom engage in long-distance travel due to the unaffordability of travel fees or costs (Casado-Díaz, 2000) . Previous studies have shown that different social-demographic groups have functional regions of different sizes (Farmer & Fotheringham, 2011) . Since a containment zone could be analogous to a functional region, the population structure should be another pivotal factor to be further considered in delineating containment zones. Restricting human movement to decrease contact probability and frequency helps mitigate large-scale epidemics. We used land-use patterns to reflect trip purposes to measure the regularity of human mobility and proposed a novel network community detection method, the Human Mobility Regularity-based Zoning (HuMoRZ) algorithm incorporating mobility regularity to delineate containment zones. Our results suggest that containment zones that incorporate mobility regularity could significantly delay the epidemic peak and critical time and decrease the severity of an epidemic. The zoning patterns proposed in our algorithm could also allow for more life functions in a zone and more evenly distributed life resources across zones than those of zones generated by other methods. We conclude that zoning with mobility regularity could narrow down possible close contacts and high-risk exposure to prioritize the deployment of screening and testing resources. It could buy health authorities more time to prepare and deploy medical resources and implement control measures against an epidemic. These findings could provide insightful implications for fighting the COVID-19 pandemic. Fei-Ying Kuo: Formal analysis, Writing -original draft, conceived of the main conceptual ideas. developed the theory, analyzed the results, and wrote the manuscript, performed the experiments in discussion. Tzai-Hung Wen: Formal analysis, Writing -original draft, developed the theory, analyzed the results, and wrote the manuscript. performed the experiments in discussions. 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